base_conv.py

#!python2
from fractions import Fraction as F

def prime_factors(n):
	#adapted from https://stackoverflow.com/a/16996439/5090149
	result=[]
	#special case: 2
	while n%2==0:
		result.append(2)
		n//=2
	d=3
	while d*d<=n:
		while n%d==0:
			result.append(d)
			n//=d
		d+=2
	return result

def base_conv(n,b,d="0123456789abcdefghijklmnopqrstuvwxyz"):
	if b<2 or b>len(d):
		raise ValueError("Invalid base")
	if isinstance(n,int) or isinstance(n,long):
		n=F(n)
	if not isinstance(n,F):
		raise ValueError("Float is not accepted; use Fraction for non-integer")
	if n<=0:
		if n==0:
			return digits[0]
		else: #negative
			return '-'+base_conv(-n,b,d)
	result=''
	if n.denominator==1: #positive integer
		while n>0:
			idx=int(n%b)
			n//=b
			result=d[idx]+result
		return result
	else: #positive non-integer
		if n>1: #has integer part
			int_part=n//1
			frac_part=n%1
			return base_conv(int_part,b,d)+base_conv(frac_part,b,d)
		else: #0.xxx
			result='.'
			denom=F(1,b)
			
			#identify recurring fractions
			pfn=prime_factors(n.denominator)
			pfb=prime_factors(b)
			pure_recurring=False
			recurring=False
			if not set(pfn)&set(pfb):
				pure_recurring=True
				recurring=True

			if not pure_recurring:
				for i in pfn:
					if i not in pfb:
						recurring=True
						break

			length_of_not_recurring_part=0
			if recurring and not pure_recurring:
				length_of_not_recurring_part=max([pfn.count(_) for _ in set(pfb)])
			
			length_of_recurring_part=0
			if recurring:
				temp=n if pure_recurring else n*(b**length_of_not_recurring_part)
				temp2=b-1
				length_of_recurring_part=1
				while (temp*temp2).denominator!=1:
					temp2=temp2*b+b-1
					length_of_recurring_part+=1
			
			if recurring:
				i=0
				while n>0:
					idx=int(n//denom)
					n-=denom*idx
					denom*=F(1,b)
					if i==length_of_not_recurring_part:
						result+='{'
					result+=d[idx]
					i+=1
					if i==length_of_not_recurring_part+length_of_recurring_part:
						result+='}'
						break
			else:
				while n>0:
					idx=int(n//denom)
					n-=denom*idx
					denom*=F(1,b)
					result+=d[idx]
			return result

if __name__=="__main__":
	print base_conv(F(123),6)
	print base_conv(F(1.25),6)
	print base_conv(F(1,5),12)
	print base_conv(F(3,2),16)
	print base_conv(F(6,5),16)
	print base_conv(255,16)
	print base_conv(F(1767707668033969,60466176),36)